How tall is your average statistics classmate? To determine this, you measure the height of a simple random sample of 38 fellow students, finding a mean height of 68 inches and a standard deviation of 2.3 inches. Construct the 95% confidence interval estimate of the population mean.
A) $68.2$ in. $

Question

How tall is your average statistics classmate? To determine this, you measure the height of a simple random sample of 38 fellow students, finding a mean height of 68 inches and a standard deviation of 2.3 inches. Construct the 95% confidence interval estimate of the population mean. 
A) $68.2$ in. $< \mu < 68.8$ in.
B) $67.2$ in. $< \mu < 68.8$ in.
C) $67.2$ in. $< \mu < 69.8 \mathrm { in }$.
D) $68.2$ in. $< \mu < 69.8$ in.

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean, we use the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the desired confidence level (for 95%, $z = 1.96$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $68 \pm 1.96\frac{2.3}{\sqrt{38}}$, we find the margin of error and then the interval, which matches the range given in option B.

How Tall Is Your Average Statistics Classmate? to Determine This 68.268.268.2

How Tall Is Your Average Statistics Classmate? to Determine This $68.2$